Sweat: One of the greatest advantages that MCP designs have is that they don't actually require the suit to be airtight. This means that small holes or damage can occur without compromising suit functionality or user health. By extension, this means that breathable fabrics can be used in their construction, and this was in fact one of the primary motivations of the original design. Someone wearing a MCP could sweat and thermo-regulate just like normal. Theoretically, a MCP suit could consist of a gas-pressurized helmet and a MCP bodysuit, above which the astronaut dons layers of extreme cold weather gear like what you'd find on arctic explorers.
Skin abrasion: An ideal MCP suit is like a second skin and does not move in relation to the wearer's skin when in use. If it can, then the suit is probably either not designed correctly or not tight enough. Speaking from personal experience with wet suits when diving, I've never had any issues with abrasion excepting where interfering with fabric layers underneath. I suspect that a well-fitting suit wouldn't have this problem.
Blood circulation: This is one of the most difficult challenges in MCP suit design. Notably, mechanical counterpressure can only be achieved with tension on parts of the body that are convex. This means places like calves, biceps, or thighs are no problem as their cross section is nearly round. Trouble spots occur in concave places such as the small of the back, armpits, backs of knees, the groin area for men and the upper torso for women. Hands and feet also have superbly complex geometry that is difficult to constrain under constant tension. This inequality in applied pressure causes problems with the blood: it pools in areas of lower pressure similar to the behavior you'd see if you stick a suction cup to your skin and pull. To counteract this, early MCP designs used foam padding to fill in concave spaces and inflatable air bladders to provide additional pressure. Nevertheless though, this problem isn't solved yet and it's likely that even someone with a modern MCP design would have visible marks where the seams or low-pressure areas of the suit are.
Dust in the environment: MCP suits have a leg up when it comes to dust because gas-pressurized suits need to keep any large bearings dust-free. Even though the bearings are doubtlessly shielded several different ways, dust (lunar dust notably) can be extremely abrasive and work itself into bearings, destroying them in an irreparable fashion. Regardless, a MCP suit would likely have a dust-proof outer layer anyways which would enable the users to take a shower or perform decontamination inside airlocks to remove any dust. Personally, I imagine a MCP suit as consisting of the MCP bodysuit, then a thermal control layer, and finally topped off with a biohazard-esque outer suit which acts as both armor against surface abrasions and an easy surface to clean.
MCP testing in the 1950's: This is covered more extensively in the Wikipedia article, but yes, long-duration tests were performed where
The longest test was two hours and forty-five minutes
and while it does not go into extensive detail, it does state that
Tests of punctures showed that up to a square millimeter of skin could be directly exposed to vacuum for extended periods with no permanent effect
Concavities or small folds in the fabric could lead to fluid pooling in the gaps
More specifically, here's an excerpt from a NASA report on the topic of the 1950's design attempts and testing:
The SAS suit posed many design challenges related to providing sufficient pressure; this manifested itself in myriad ways throughout development including:cardiovascular congestion, syncope, poor circulation, pain, petechiae, fatigue, increased heart rate,decreased respiratory capacityand swelling.Many of these issues could not be eliminated over the course of SAS development.